Correlation between conduction electrons and electronic orbitals leads to interesting materials properties such as metal-insulator transitions, colossal magneto resistance and superconductivity. Aspheric electronic orbitals, characterized by their quadrupole moment, may order and cause partial charge localization of the conduction electrons or mediate coupling between cooper pairs.
Orbital order in f electron materials is dominated by coupling with the lattice (Jahn-Teller) or by indirect Coulomb interactions via the conduction electrons.
The large orbital momentum of the f electronic shell also gives rise to a significant influence of higher multipole moments and may lead to hidden order phase transitions as demonstrated in the extensively studied URu2Si2. Therefore it is important to understand the quadrupolar and higher order multipole pair interactions in these materials.
Resonant and non-resonant Bragg diffraction has been used to study orbital order of DyB2C2 and TbB2C2. The theoretical description of resonant Bragg diffraction at the Dy M4,5 edge is extended to include the interaction between the 4f quadrupole and the 3d core state. This leads to the determination of the higher order multipole moments of the Dy 4f shell.
TbB2C2 is proposed to exhibit a transition from antiferromagnetic (AFM) to antiferroquadrupolar (AFQ) order in an applied magnetic field. We find that the Tb 4f quadrupolar pair interaction depends on the specific orientation of the orbitals as predicted theoretically and can be manipulated with an applied magnetic field.